Operations in the correct order

When you are faced with a mathematical expression that has several operations or parentheses, the solution may be affected by the order in which you tackle the operations. For example, take the expression

4·7-24\cdot 7-2

If we do the multiplication first, we arrive at the following answer:

28-2=2628-2=26

If instead we begin by substracting, we get:

4·5=204\cdot 5= 20

In order to avoid confusion and to ensure that everyone always arrives at the same result, mathematicians established a standard order of operations for calculations that involve more than one arithmetic operation. Arithmetic operations should always be carried out in the following order:

  1. Simplify the expressions inside parentheses ( ), brackets [ ], braces { } and fractions bars.
  2. Evaluate all powers.
  3. Do all multiplications and divisions from left to right.
  4. Do all additions and subtractions from left to right.

Example

Suppose you want to figure out how many hours a person works in two days assuming that they work 4 hours before lunch and 3 hours after lunch each day. First, work out how many hours the person works each day:

4+3=74+3=7

and then multiply that by the number of days the person worked:

7·2=147\cdot 2=14

If we were to write this example as one expression, we would need to use parentheses to make sure that people calculate the addition first:

4+3·2=14\left ( 4+3 \right )\cdot 2=14


Video lesson

Simplify the following expression:

2·8-3+6·2-32\cdot\left [ \left ( 8-3 \right )+6\cdot \left ( 2 \right ) \right ]-3